Tethered Monte Carlo: Managing Rugged Free-Energy Landscapes with a Helmholtz-Potential Formalism

Martı́n-Mayor, V.; Seoane, Beatriz; Yllanes, David

doi:10.1007/s10955-011-0261-4

Cited by 10 publications

(18 citation statements)

References 92 publications

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“…To tackle with thermalization issues, we apply the reversible Event Chain Monte Carlo (ECMC) algorithm 42,43 (with a slight variation to account for the cN immobile variables 44 ), which represents a gain of a factor 10 in times with respect to standard Monte Carlo (MC) moves. In addition to that, we used the tethered MC method 45 to quantify the relative weight between the L and G phases without waiting for the occurrence of spontaneous activated events during the dynamics. The tethered strategy 45 relies on independent simulations at fixed values of the order parameter, in this case the overlap Q(C, C 0 ) between the running configuration C and the reference one C 0 (the overlap is defined as Q(C,…”

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confidence: 99%

First-principles computation of random-pinning glass transition, glass cooperative length scales, and numerical comparisons

Cammarota

Seoane

2016

Phys. Rev. B

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As a guideline for experimental tests of the ideal glass transition (Random Pinning Glass Transition, RPGT) that shall be induced in a system by randomly pinning particles, we performed first-principle computations within the Hypernetted chain approximation and numerical simulations of a Hard Sphere model of glass-former. We obtain confirmation of the expected enhancement of glassy behaviour under the procedure of random pinning, which consists in freezing a fraction c of randomly chosen particles in the positions they have in an equilibrium configuration. We present the analytical phase diagram as a function of c and of the packing fraction φ, showing a line of RPGT ending in a critical point. We also obtain first microscopic results on cooperative lengthscales characterizing medium-range amorphous order in Hard Spere glasses and indirect quantitative information on a key thermodynamic quantity defined in proximity of ideal glass transitions, the amorphous surface tension. Finally, we present numerical results of pair correlation functions able to differentiate the liquid and the glass phases, as predicted by the analytic computations. PACS numbers: Valid PACS appear hereA common feature of liquids deep below the melting point (supercooled) is the remarkably steep increase of relaxation time, until the system falls out of equilibrium at a conventional temperature T G . Since decades, it is present in the literature the claim of the possible presence of a phase transition 1,2 , the ideal glass transition (IGT), underlying the dynamical arrest and located at a lower temperature T K . Despite the first formulation of a consistent phenomenological thermodynamic picture 3 this intuition remained at length debated for the lack of other indicators of the imminent thermodynamic singularity. In this context, other theoretical perspectives based on dynamic or topological approaches, sometimes excluding the presence of any transition, have been proposed as alternative explanations of the sluggish dynamics 4,5 . In recent times, new important results have been obtained in the development of the thermodynamic scenario. We particularly refer on the one hand, to the first definition and measure of a new kind of cooperative length-scale 6,7 detecting the spatial extent of amorphous order 8 , called point-to-set l P S , and on the other hand, to the development of a field theory description of the IGT in terms of a suitable large deviation function 9-11 and the introduction of perturbative 12,13 and non-perturbative 14,15 fluctuations in this description. In view of a full fledged theory of glass-formers and quantitative predictions of their properties, these advancements have been corroborated by the formulation of a microscopic theory [16][17][18][19] inspired to classical firstprinciple computations techniques in liquids 20,21 . Due to particularly severe critical properties of the IGT, i.e. an exponential growth of relaxation time and a power law increase of the cooperative length, the revealing of its properties still rema...

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Section: Pacs Numbers: Valid Pacs Appear Herementioning

confidence: 99%

First-principles computation of random-pinning glass transition, glass cooperative length scales, and numerical comparisons

Cammarota

Seoane

2016

Phys. Rev. B

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“…However, in the last years, constrained Monte Carlo (MC) methods have been proposed as a solution to compute this W (q) [12,13]. Here we propose a recent constrained MC method, the tethered method [35], originally proposed for spin lattice systems [17][18][19] but recently applied to hard spheres [20]. This method presents a major simplification of standard umbrella sampling method [21][22][23] since the potential differences are very precisely computed from a thermodynamic integration, thus avoiding the tedious multi histogram reweightings.…”

Section: Pacs Numbersmentioning

confidence: 99%

Liquid-glass transition in equilibrium

Parisi

Seoane

2014

Phys. Rev. E

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We show in numerical simulations that a system of two coupled replicas of a binary mixture of hard spheres undergoes a phase transition in equilibrium at a density slightly smaller than the glass transition density for an unreplicated system. This result is in agreement with the theories that predict that such a transition is a precursor of the standard ideal glass transition. The critical properties are compatible with those of an Ising system. The relations of this approach to the conventional approach based on configurational entropy are briefly discussed. PACS numbers:Glass forming materials display a rapid growth of the viscosity upon cooling [1]. Dynamics is dramatically slowed down, but this fact is not accompanied by any obvious structural or thermodynamic change [2]. As a consequence, below certain temperature, the liquid gets trapped in a solid like amorphous configuration for a very long time. From the experimental point of view, these systems live permanently out of equilibrium: it is natural to ask whether this phenomenon is a consequence of a thermodynamic transition or, in contrast, whether it is just a pure dynamical arrest process [3]. Different mean field approaches, from the Adam-Gibbs theory [4], to the mode coupling theory [5] or the spin-glass theory [6] agree on the existence of an "ideal structural glass transition" in the infinite time limit, but the validity of this claim for realistic systems is still under debate; other interpretations of the phenomenon where no transition is present have been proposed [7].Under the mean field approximations, supercooled liquids undergo a random first order transition (RFOT) [8,9], which corresponds to "one-step replica symmetry breaking" [6]. In this scheme, below certain temperature T c , the ergodicity is lost due to the appearance of an exponentially large number of metastable states. The system gets trapped in one of them (not necessarily the thermodynamic) and the large relaxation times are thus related to the escape times. The Kauzmann-like entropy crisis may take place at T K (< T c ), the point where the ideal glass phase becomes the thermodynamic one.The properties of this transition can be studied (at fixed density ρ) by considering the replica potential W (q) (i.e., the free energy) as a function of the degree of similarity between all the possible amorphous configurations [10]. In analogy with spin glasses, the chosen order parameter is the "overlap" (q) between the configurations of two equilibrium systems ("replicas"). A key prediction of the theory is that one can observe a precursor of the phase transition in the shape of this potential still deep in the liquid phase. Indeed, the glass transition is characterized by a sharp decrease of the number of available states, which should be detected by the appearance of second minima in W (q) at large q. In contrast to ordinary first order transitions, these two minima are not related to different phases but to similar and completely different configurations. In the RFOT approach this transit...

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“…With the exception of [15], the different estimations of p co are compatible, although with widely differing accuracies.The computation of the interfacial free energy, γ, is more involved, since the issue of spatially heterogeneous mixtures of fluid and solid can no longer be skipped (as done in equilibrium computations of p co ). Indeed, recent estimations are either precise but mutually incompatible [23,24], or of lesser accuracy [25].Here, we introduce a tethered MC [26,27] approach to HS crystallization. The correct crystal appears in our simulation by constraining the value of two order parameters.…”

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“…The tunable parameter α tightens the quasi-constraints (we choose α = 200 [27]). Exchanging the integration order in (1) yields…”

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Equilibrium Fluid-Solid Coexistence of Hard Spheres

et al. 2012

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We present a tethered Monte Carlo simulation of the crystallization of hard spheres. Our method boosts the traditional umbrella sampling to the point of making practical the study of constrained Gibbs' free energies depending on several crystalline order-parameters. We obtain high-accuracy estimates of the fluid-crystal coexistence pressure for up to 2916 particles (enough to accommodate fluid-solid interfaces). We are able to extrapolate to infinite volume the coexistence pressure (pco = 11.5727(10)kBT /σ 3 ) and the interfacial free energy (γ {100} = 0.636(11)kBT /σ 2 ).PACS numbers: 05.10. Ln, 64.60.My, Crystallization is a vast field of research, where experiments and theory cross-fertilize. Hard-spheres (HS) provide a celebrated example: the numerical finding of a fluid-solid phase transition [1] motivated experiments on colloids [2,3]. Finding an accurate procedure to locate the equilibrium phase boundaries for HS is a crucial step to address the self-assembly of complex molecules [4], as modeled by HS plus non-spherical interactions (e.g patchy [5] and Janus particles [6]).Up to now, numerical simulations of crystallization phase transitions have been well behind their fluid-fluid counterpart (e.g. vapor-liquid equilibria [7]). Actually, HS are the preferred benchmark for numerical approaches to crystallization. Yet, the lack of exact solutions enhances the importance of accurate numerical and/or experimental studies.However, for preexisting numerical methods, a simulation whose starting configuration is a fluid never reaches the equilibrium crystal. Much as in experiments [3], the simulation gets stuck in a metastable crystal, or a defective crystal (or even a glass [8]). The proliferation of metastable states defeats optimized Monte Carlo (MC) methods that overcome free-energy barriers in simpler systems [9][10][11]. Besides, experimental and numerical determinations of the interfacial free energy are plainly inconsistent (maybe due to a small electrical charge in the colloidal particles [12]).Since feasible numerical methods [13] could not form the correct crystalline phase spontaneously, choosing the starting particle configuration became an issue (e.g. crystalline or a carefully crafted mixture of solid and fluid phases). Methods can be classified as equilibrium or nonequilibrium. In the phase switch MC [14], one tries to achieve fluid-crystal equilibrium (only up to N = 500 HS [15] As for the accuracy, in equilibrium computations the coexistence pressure p co was obtained with precisions of ∼ 0.1% (at finite N ). Yet, the N values that can be simulated are rather small. An N → ∞ extrapolation is mandatory, which degrades the final accuracy to ∼ 1% [14,15,19] (results are summarized in Table I). The situation improves by an order of magnitude for the direct-coexistence method. With the exception of [15], the different estimations of p co are compatible, although with widely differing accuracies.The computation of the interfacial free energy, γ, is more involved, since the issue of spatially heterogen...

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Tethered Monte Carlo: Managing Rugged Free-Energy Landscapes with a Helmholtz-Potential Formalism

Cited by 10 publications

References 92 publications

First-principles computation of random-pinning glass transition, glass cooperative length scales, and numerical comparisons

First-principles computation of random-pinning glass transition, glass cooperative length scales, and numerical comparisons

Liquid-glass transition in equilibrium

Equilibrium Fluid-Solid Coexistence of Hard Spheres

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